Comments for Some Classical Maths
https://someclassicalmaths.wordpress.com
Wed, 27 Apr 2011 12:39:16 +0000hourly1http://wordpress.com/Comment on The irrational nature of zeta(3) by Cliff Bott
https://someclassicalmaths.wordpress.com/2009/08/02/the-irrational-nature-of-zeta3/#comment-56
Wed, 27 Apr 2011 12:39:16 +0000http://someclassicalmaths.wordpress.com/?p=152#comment-56Thanks Andrew. I have now fixed the way my name displays. I’m a mathematical hobbyist, not a prefessional mathematician, so I’m not sure I can help you with the question, but I’ll try to have a look at it and think about it over the next couple of weeks. I’ll try to email separately in case you don’t see this comment.
]]>Comment on The irrational nature of zeta(3) by Andrew
https://someclassicalmaths.wordpress.com/2009/08/02/the-irrational-nature-of-zeta3/#comment-55
Wed, 27 Apr 2011 08:48:57 +0000http://someclassicalmaths.wordpress.com/?p=152#comment-55Hi once again!
I’m sorry for not realising that your name is Cliff Bott in itself (I thought that the bott was a truncation of our surname).
I’d like to ask you something that occurred to me while perusing Sierpinski’s “Pythagorean Triangles”:
The T-ratios of any Pyth. triangle are rational. So, we can say that the acute angles are necessarily irrational. But can we say that they are irrational multiples of pi? Or what can one say, at best?
Sincerely,
Andrew
]]>Comment on The irrational nature of zeta(3) by Andrew
https://someclassicalmaths.wordpress.com/2009/08/02/the-irrational-nature-of-zeta3/#comment-54
Wed, 27 Apr 2011 08:29:02 +0000http://someclassicalmaths.wordpress.com/?p=152#comment-54Dear Cliffbott,
Thank you for this post. I always wondered just how accessible the proof of the irrationality of zeta(3) would be. From the pdf that I’ve downloaded, it seems like I’ll be able to follow it.
My interest in irrationals and transcendentals stems from Niven’s delightful first book (No. 1 in the NML series). Will move on to his later (Carus Monograph) book as well as Gelfond’s book from the same age (half a century ago).
Hope you keep enjoying your Mathematics!
Sincerely,
Andrew
]]>Comment on Lindemann-Weierstrass Theorem by cliffbott
https://someclassicalmaths.wordpress.com/2010/02/06/lindemann-weierstrass-theorem/#comment-13
Wed, 18 Aug 2010 10:26:48 +0000http://someclassicalmaths.wordpress.com/?p=599#comment-13Thank you for your comment Sandeep. I hope the posts were of use to you. At the moment I am looking at Roger Apéry’s proof of the irrationality of zeta(3) and have become rather bogged down in it. But I think I can see the light at the end of the tunnel. After that I want to examine the connections between irrationality proofs using continued fractions, and those using repeated integration by parts. This will keep me busy for some time to come, so I’m afraid it will be some time, if ever, that I come to Mahler’s classification.
]]>Comment on Lindemann-Weierstrass Theorem by Sandeep
https://someclassicalmaths.wordpress.com/2010/02/06/lindemann-weierstrass-theorem/#comment-12
Tue, 17 Aug 2010 20:59:55 +0000http://someclassicalmaths.wordpress.com/?p=599#comment-12I came across your blog while looking for simplified proofs on transcendence. Just thought I’d leave a comment to convey my appreciation. Perhaps you could shed some light on Mahler’s classification of transcendental numbers in the next few posts.
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